I have a question about the really meaning of the fine structure constant. Actually, my doubt is why the physicist look to a meaning for this constant.
I understand the difference between this constant and the ordinary constant, that is, it carry no units with it.
But is not this just like pi or euler number? It sometimes appears in physics situations too, without units, but nobody looks for its "meaning" as much as looking for that of the fine structure constant (As Far As I Know).
As we can just sit and accept the importance of pi, the importance of euler number, why we need to find a meaning to the fine structure and not just sit and accept its importance too?
[Physics] The fine structure constant
atomic-physicsdimensional analysisphysical constantsquantum mechanics
Best Answer
Mathematical constants such as $\pi$ and $e$ have values that are determined by their definitions. For example, you can define $\pi$ as the ratio of the circumference of a circle to its diameter, and then use this definition to calculate $\pi$ to as many decimal places as you want. Constants like this cannot have any other value than the value they have.
By contrast, we know of no reason why the fine structure constant has the value it has. And we can imagine a universe in which it has a different value. So this leads physicists to wonder why it is approximately $1/137$ instead of, say, $1/140$, or something much smaller or much larger.
In short, dimensionless physical constants are not mathematical constants. Or at least they aren’t in our current physical theories. Instead they are simply parameters of our models.